If you want air conditioning without any AC power source, you really have two options - an AC-operated air conditioner powered by a big battery and an inverter, or a DC-operated ir conditioner powered by a big battery, without an inverter. Inverters have some power loss, so getting it out of the equation isn't a bad idea. If your original TM air conditioner has died and you are thinking of retrofitting a DC-operated unit, it may be a good solution. But a retrofit can be tough to do, and the results may not be as rosy as the advertising promises. If you are seriously considering a retrofit, keep reading. Otherwise, you can probably skip it - it is not hard reading, but I know it is long.
DC-operated air conditioners were originally made for cooling the cab of big over-the-road diesel trucks during a layover. By law, the driver can drive only a certain number of hours per day, and the rest of the day must lay up somewhere. For a long time, most big rigs were not equipped with a conventional belt-driven air conditioner on the engine. Cooling the cab during the layover was a big deal, and electrically powered retrofits were attractive.
Big diesel trucks make DC air conditioner retrofits reasonably easy. Most trucks have powerful electrical systems because of all the exterior lights, so they have big alternators, capable of enough power to run an air conditioner for hours at a time. Also, the tractor has plenty of space in the engine compartment for the big cables (#6 or larger) needed by the heavy current used by a DC air conditioner. And the cab is a reasonably small space, so it doesn't require a lot of BTUs of cooling. Perhaps their biggest advantage is that a big diesel engine can idle for hours during a layover, while using only a tiny amount of fuel. And while it is idling, the alternator is generating power. DC-powered air conditioners are a natural fit for big trucks.
Some of those factors work against a TM retrofit. First, you don't have a big alternator to power the air conditioner, and even if you did, you can't let the engine idle for hours while you are camping. So you need a very large battery to provide stored power to the air conditioner. Solar may extend the battery a bit, but it won't carry it. Second you need to run really big power cables from the battery (wherever it is) to the air conditioner on the roof, and that can be really hard since you can't run them inside the walls or roof. Third, the interior space of a truck cab, even a cab with a sleeper, is smaller than a TM. A 10,000 BTU air conditioner may be enough for a truck cab, but it may be marginal for a TM.
The original DC air conditioners were basically a 120 volt AC-powered unit, with new DC motors for the compressor and fan. The actual cooling mechanism didn't change much, so the power consumption (in BTUs per watt) is the same for AC and DC. So for a given number of cooling BTUs out - say 15,000 BTUs - both units will consume about the same number of watts. But remember that the most basic rule of electricity is that Watts = Volts X Amps. So if you cut the volts from 120V to 12V (a factor of 10) then you have to increase the amps (current) by a factor of 10 to get the same number of watts, and the same number of BTUs. At 10X, the number of amps gets really big. This 10X current requirement is what drives the need for very large #6 or #4 cables.
This is not meant to be either encouraging or discouraging in regard to DC air conditioners. But it is intended to point out some of the advantages and some of the difficulties. Most of all, it is intended to help you make your decision in the face of all the advertising hype. The manufacturers will throw around magic words like "efficient" and "easy" and "small" and "smooth", but as in all advertising, you should not expect the results to be magic. I hope this helps balance the scale.